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 TMF, 1971, Volume 8, Number 2, Pages 175–191 (Mi tmf4396)

Axiomatic field theory in terms of operator Jacobi matrices

Yu. M. Berezanskii, V. D. Koshmanenko

Abstract: It is shown that the Wightman axiomatic theory of an tlermitian scalar field can be reformulated in terms of operator Jacobi matrices in analogy with the transition to Jacobi matrices in the problem of moments. This reformulation ieads naturally to the concept of a quasifield, an object that is simpler than a field. The generating funetionals that define the quasifield and are reiated to the Wightman functionals are studied. In the case of a free field, specification of the latter by creation and annihilation operators is identical with the specification in terms of Jacobi matrices.

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English version:
Theoretical and Mathematical Physics, 1971, 8:2, 754–765

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Citation: Yu. M. Berezanskii, V. D. Koshmanenko, “Axiomatic field theory in terms of operator Jacobi matrices”, TMF, 8:2 (1971), 175–191; Theoret. and Math. Phys., 8:2 (1971), 754–765

Citation in format AMSBIB
\Bibitem{BerKos71} \by Yu.~M.~Berezanskii, V.~D.~Koshmanenko \paper Axiomatic field theory in terms of operator Jacobi matrices \jour TMF \yr 1971 \vol 8 \issue 2 \pages 175--191 \mathnet{http://mi.mathnet.ru/tmf4396} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=471742} \transl \jour Theoret. and Math. Phys. \yr 1971 \vol 8 \issue 2 \pages 754--765 \crossref{https://doi.org/10.1007/BF01037996}